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charlettethomap7e9st
22.04.2020 •
Mathematics
Graph the line that passes through the points (3, -2)(3,−2) and (9, 2)(9,2) and determine the equation of the line.
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Ответ:
2x -3y = 12
Step-by-step explanation:
For some horizontal change Δx and some vertical change Δy between the two points, an equation of the line through points (x1, y1) and (x2, y2) can be written as ...
Δy·x -Δx·y = Δy·(x1) -Δx·(y1)
Here, we have ...
Δy = y2 -y1 = 2 -(-2) = 4
Δx = x2 -x1 = 9 -3 = 6
So, our equation can be ...
4x -6y = 4·3 -6·(-2) = 24
Factoring out a common factor of 2 makes the equation be ...
2x -3y = 12 . . . . . . equation of the line in standard form
Solving for y gives the equation in slope-intercept form:
y = 2/3x -4
_____
More conventional solution
Plotting the points and drawing the line, you see that the y-intercept is -4. You also see that there is a "rise" of 2 grid squares for each "run" of 3 grid squares. Thus the slope of the line is 2/3. With this information, you can write the equation directly in slope-intercept form:
y = mx + b . . . . . . line with slope m and y-intercept b
y = 2/3x -4 . . . . . . the line through the given points
Ответ:
Step-by-step explanation:
Let's turn this equation into slope-intercept form.
Thus, the slope is -2 and the y-intercept is 2/3